If you tell a football team often enough that they are the best in the world, by which you really mean that their attacking players win matches by scoring goals more beautifully than anyone else around, there is a chance their defenders may believe it applies to them, too. Then they may fall into the sort of trap sprung by Arsenal last night at the pulsating, heart-in-mouth climax of a match that had spent most of 80 minutes deceiving us into thinking it was proceeding to the orderly and logical conclusion of a Barcelona victory.

Brilliantly taken goals in the last 12 minutes from Robin van Persie, so profligate in the early stages, and Andrey Arshavin, who has hardly had a decent kick all season, gave Arsenal a 2-1 lead that they will take into the second leg of their round-of-16 tie at the Camp Nou on 8 March, and which offers them a credible chance of a place in the quarter‑finals.

Be honest, now. Before last night's match had taken its final convulsive twist, were Arsène Wenger's bunch of lightweights and fancy-pants the team you would choose to fight for your life in the last dozen minutes of a crucial tie? Opinions in that particular debate may have to be swiftly revised. Even Sir Alex Ferguson would have to admire the guts that swept the north London side from a losing position to a tumultuous victory against the most daunting opposition available in world football.

Though it has not in itself guaranteed a trophy, this could be accounted the finest single victory of Wenger's 14 years in charge at Highbury and the Emirates. From measuring success against Barcelona only in terms of stronger resistance than they were able to show in their 6-3 aggregate defeat at the hands of the same opponents last year, they were able to make the transition to looking their opponents squarely in the eye and leaving the field after shaking their hands as winners.

As for Barcelona, now they know they have a fight on their hands when Arsenal arrive in the Catalan capital next month. Had they preserved the 1-0 lead given them by David Villa midway through the first half, they might have been able to cruise through the second leg. Instead the last-ditch collapse of their defence means they will not be able to rely on tieing up their opponents in a web of endless ball retention, but must come out and score goals. At which, it will be remembered, they are generally rather good.

And there will be, of course, unbounded satisfaction in Arsenal's corner of the capital that they have managed to steal the thunder of their neighbours. Only 24 hours earlier Tottenham Hotspur earned their own historic first-leg victory against Milan, seven times winners of the European Cup, in Italy. With Chelsea facing FC Copenhagen next week, now London – which has never produced a European Cup-winning side – is contemplating a decent chance of sending three teams into the last eight.

How remote such a possibility had seemed in the early stages, even though the home side had begun by fulfilling Samir Nasri's promise that they would not be the "naive Arsenal" of 10 months ago. After Barcelona had opened the match with several suave passages of uninterrupted possession, Arsenal began to give as good as they were getting, with Theo Walcott and Jack Wilshere, their two young Englishmen, at the heart of their most telling efforts.

Walcott jinked his way into the penalty area with a multidirectional dribble that immobilised the jade‑shirted defenders before Cesc Fábregas refined the move with a chip to Van Persie, who was unable to beat Víctor Valdés.

The Dutchman was more wasteful when he sliced his shot wide from a perfect position after the defence had been dismantled by a thrilling run and exquisite pass from Wilshere, who won the ball cleanly and distributed it with lethal accuracy all night.

But Barcelona are still Barcelona, able at any time to create panic and despondency through the consistent application of sheer quality, and no football stadium containing 60,000 people can have fallen as silent during play as the Emirates after 15 minutes, when Lionel Messi stunned Andrés Iniesta's pass back to Villa, accepted the immediate return and broke clear to the left of the Arsenal goal.

A frozen hush settled over the ground as the little Argentinian genius closed on the transfixed Wojciech Szczesny. Messi had been thoughtful enough to wear bright orange boots, lest anyone should find it difficult to recognise his Beatle haircut or his uniquely sudden movements, like a little rag doll being jerked into life by an electric current. Now he measured a gentle chip to his own exacting standards, delivered it as gently as though he were wearing satin slippers, and then watched with horror as the ball rolled just wide of the far post.

This was not, after all, destined to be Messi's 41st club goal of the season but one of his much rarer misses. North London let out a gasp of relief and started breathing again. Arsenal's worst fears had been temporarily averted, although not for long. And there was another hour of agony to go – including, amazingly, another Messi miss: two chances, no goals, disbelief all round – before deliverance arrived.

First Van Persie, from the most acute angle, produced a shot of unearthly penetration. Then it was left to Arshavin, so often disappointing in recent months, to strike the blow that will resound around Europe.